An Inverse Nash Mean Field Game-based Strategy for the Decentralized Control of Thermostatic Loads

Thermostatic loads have long been recognized as a useful resource for shaping aggregate load dynamics and for mitigation of intermittency in solar and wind based renewable generation. When considering the residential sector, there can be millions of such loads, each with a very small contribution but can be collectively coordinated. Mean field game (MFG) theory has emerged as a natural tool for mathematically capturing this framework. While most existing works on MFG analysis start from agent cost functions to identify the properties of potential Nash equilibria and the associated agent control laws, this work differs in that an inverse process is followed. We reverse engineer the agent cost functions so that, while remaining comfort sensitive, they are guaranteed to lead via decentralized control laws to a precalculated Nash equilibrium. The latter is desirable from an aggregator's point of view. The approach is illustrated in the case of a power reduction objective for a collection of thermal loads. Furthermore, to effectively manage the impacts of load control actions in a power distribution network, it is shown how the control efforts can be adjusted on a nodal basis using voltage sensitivities.